Simplify $\frac{180}{16}\cdot \frac{5}{120}\cdot \frac{8}{3}$.
Explanation: We can see that $180$ and $120$ have a common factor of $60$.  Also, note that $16$ and $8$ have a common factor of $8$.  This means we can simplify to get $$\frac{180}{16}\cdot \frac{5}{120}\cdot \frac{8}{3}=\frac{\cancelto{3}{180}}{\cancelto{2}{16}}\cdot \frac{5}{\cancelto{2}{120}}\cdot \frac{\cancel{8}}{3}=\frac{3}{2}\cdot \frac{5}{2}\cdot \frac{1}{3}.$$Now, notice that we can cancel the factor of $3$ in the numerator and the denominator.  Therefore, we have $$\frac{3}{2}\cdot \frac{5}{2}\cdot \frac{1}{3}=\frac{\cancel{3}}{2}\cdot \frac{5}{2}\cdot \frac{1}{\cancel{3}}=\frac{5\cdot 1}{2\cdot 2}=\boxed{\frac{5}{4}}.$$